Arsene Wenger's side are a point behind Chelsea in second place after a frantic evening in which neither side truly dominated a match low on the quality expected from these teams.
In truth, United probably had the two best chances of the match, but home goalkeeper Wojciech Szczesny was up to the task on the night in making two fine stops by denying Robin van Persie a goal against his former club.
Szczesny made a fine diving stop in the opening minute to save from Van Persie while he tipped a powerful header from the Dutch forward onto the bar from a Wayne Rooney cross after a fabulous sweeping move on the break by the visitors.
United manager David Moyes extends his record to 49 Premier League matches without victory in away matches at a traditional big four of Arsenal, Chelsea, Liverpool or Manchester United - though he spent over a decade in charge of Everton.
More importantly, United are 11 points behind fourth-placed Liverpool in the hunt for a Champions League spot after their 3-2 win at Fulham elsewhere on the night.
1' - CHANCE FOR VAN PERSIE: Glorious chance for Van Persie. Error by Arteta, but the Dutch forward drives the ball straight into the arms of Wojciech Szczesny.
62' - VALENCIA TO THE RESCUE FOR UNITED: Valencia heads off the line from the Laurent Koscielny header. Lovely corner by Ozil. Arsenal so close to the opening goal.
77' - GIROUD NARROWLY FAILS TO CONNECT: Glorious ball into the box by Sagna, but Giroud just fails to connect with the cross. Not sure Vidic would have made the interception.
79' - SZCZESNY WITH AN EXCELLENT STOP: Szczesny nudges the Van Persie header onto the bar from the Rooney ball. Some superb play by Carrick and Rooney on the break. United so close to the opening goal.
83' - DE GEA COMES TO THE RESCUE: Excellent save by De Gea diving low to his right to claw out the shot by Cazorla. Fine piece of attacking play by Arsenal, but excellent stop by De Gea.
88' - ARSENAL SEARCH FOR THE WINNING GOAL: Another brilliant header clear by Vidic under pressure from Mertesacker in the United area before De Gea dives to his left to make a fine stop from the Cazorla hit.
Arsenal have kept 11 clean sheets in their last 12 home matches in all competitions, conceding just one goal in that time – in the 1-1 Premier League home draw v Everton on December 8.
Arsenal have failed to score in both Premier League matches against Man Utd for the first time since 2005/06 – and for the fourth time in the Division overall (also 1992/93 & 1994/95).
For the first time since 3 January 2006 and only the second time in the Premier League era this exact fixture in the Premier League ends goalless.
Was it a better point for Arsenal or United? You have to say United and Moyes will be content with their lot before they set off for a training break in Dubai. United set up not to lose while hitting on the break and a draw was a productive outcome from their trip to London. Arsenal will rue failing to dislodge Chelsea from top place, but at least they did not lose. Which was important after they were thumped 5-1 by Liverpool at the weekend.
MAN OF THE MATCH
Nemanja Vidic (Manchester United): A tough old evening for Vidic, but he was back to something like his best form in coping with the considerable presence of Arsenal forward Olivier Giroud.
Arsenal: Szczesny 8, Sagna 7, Mertesacker 7, Koscielny 7, Gibbs 7, Arteta 6, Wilshere 6, Rosicky 6, Ozil 6, Cazorla 6, Giroud 6. Subs: Oxlade-Chamberlain 6.
Manchester United: De Gea 7, Rafael 5, Smalling 6, Vidic 8, Evra 4, Valencia 6, Cleverley 6, Carrick 7, Mata 6, Rooney 7, Van Persie 6. Subs: Ferdinand 7, Young 6, Januzaj 6.
THE MATCH IN A TWEET